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H2M 2019 Paper 1 Question 7

H2M 2019 Paper 1 Question 7
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2020-06-18 13:06
TrigonometryCalculusDerivative
This example demonstrates the solution process of H2M 2019 Paper 1 Question 7. Key mathematical concepts include derivatives, similarity transformations, and trigonometric functions. Using commands like Tangent, Solutions, Angle, If, etc., a geometric figure involving derivatives and trigonometric functions is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Tangent((b1, f1(b1)), f1) → h1
  2. Tangent(((-b1), f1((-b1))), f1) → i1
  3. Solutions(g1 = 0) → l1
  4. Angle(h1, i1) → β1
  5. Tangent(((-b2), f2((-b2))), f2) → i2
  6. Tangent((b2, f2(b2)), f2) → h2
  7. Angle(h2, i2) → β2
  8. If(d ≟ 1, f1, f2) → f
  9. If(d ≟ 1, h1, h2) → h
  10. If(d ≟ 1, i1, i2) → i
  11. If(d ≟ 1, β1, β2) → β
  12. If(d ≟ 1, g1, g2) → g
  13. If(d ≟ 1, SurdText[Slope[i1], {ℯ}], SurdText[Slope[i2], {ℯ}]) → text1
  14. If(d ≟ 1, SurdText[i1(0), {ℯ}], SurdText[i2(0), {ℯ}]) → text2
  15. If(d ≟ 1, SurdText[h1(0), {1 / ℯ}], SurdText[h2(0), {1 / ℯ}]) → text3